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>postscript: mathematically inclined readers of the
>optimal-f books have surely noted another difference:
>optimal-f gets the same final equity (so called TWR)
>for a sequence of trades REGARDLESS OF THE ORDER IN
>WHICH THE TRADES OCCUR. But since Fixed Ratio
>explicitly looks at equity history, it gives different
>final equity results for different orderings of the
>same sequence of trades. I will leave it for you
>to ponder whether this is a bug or a feature :-) .
>
Premise of optimal-f is (statistical) independance of trade results. In this
case, optimal-f will yield maximum TWR. If there is some trade sequence
dependance, meaning a win is more likely to be followed by another win,
etc., you can either:
1) Incorporate that info into a varied fractional as opposed to a fixed
fractional bet-sizing algorithm and possibly end of with a bigger TWR than
optimal-f.
2) Incorporate this dependance into the system *before* applying any
bet-sizing algorithms and then use optimal-f.
Number 2) will result in a higher TWR. So optimal-f wins again.
Real people can't handle gigantic drawdowns, so Jones devised his fixed
ratio algorithm. It sacrifices (possibly) TWR for buffered drawdowns. I say
possibly because it depends on the sequence of trades. On any given sequence
of trades, fixed ratio may yield a higher TWR than optimal-f due to a
favorable ordering of trade results. However, if you took the average of all
possible trade sequences using fixed ratio and compared this to optimal-f,
optimal-f wins again.
Scott Hoffman
Issaquah, WA
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